I was trying to build a circuit that if switched on would slowly (in span of of 1~5s) light up around 20 LEDs - progressively, not all at once.

To achieve that i used one capacitor to initiate the "build up" effect (and discharge when switched off) and then used NPN transistor's emitter as a base input for next transistor, as shown on diagram below.

It works but with each consecutive "part" the light is dimmer and fades out completely after 3rd LED. Which leads me to suspect that power on base of transistor is getting weaker - but it shouldn't require much to let power through.